On a precise check of the standard model in an experiment with a 90Sr beta source

A discussion is given on the prospects for making a precise determination of the value of sin²θ _W (θ_W is the Weinberg angle) and for improving the sensitivity of the search for the antineutrino magnetic moment to ≈1.5×10⁻¹¹μ_B and for the mixing parameter to sin²2θ ≈10⁻² by measuring in a single experiment the cross sections for scattering for the reaction . Such an experiment with ∼100 000 events/yr detected for each reaction can be carried out, for example, using the BOREXINO detector and an approximately 10 MCi ⁹⁰Sr source. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 435–439 (10 April 1998)     

Search for anomalous carbon atoms — evidence of violation of the Pauli principle during the period of nucleosynthesis

A search for anomalous carbon atoms — atoms with three K-shell electrons — is made by γ-activation analysis of boron with the impurity carbon removed radiochemically. A limit on the existence of such atoms was determined: . This corresponds to a limit on the lifetime with respect to violation of the Pauli principle by electrons in a carbon atom of τ⩾2×10²¹ yr. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 2, 104–108 (25 July 1998)     

On the effect of a magnetic field on the yield point and kinetics of macroplasticity in LiF crystals

A strong effect of a static magnetic field B on active deformation kinetics ( =const) in LiF crystals is observed. This is a threshold effect with respect to B and ; it is observed only for B> B _c (B≃0.4 T) and . Magnetic sensitivity is exhibited by the yield stress τ _y , which decreases by approximately a factor of 1.5 for B=0.48 T, and by the stage-II and stage-III hardening coefficients θ_II and θ _III, the former decreasing and the latter increasing in a magnetic field. A physical interpretation is proposed for the observed behavior. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 470–474 (25 March 1997)     

Using the e ± μ? + E Tmiss signature in the search for supersymmetry and lepton-flavor violation in neutralino decays

The LHC (CMS) discovery potential in the search for supersymmetry and lepton-flavor violation in neutralino decays using the e ^± μ^∓ + E _T ^miss signature is studied. A detailed study is done for the CMS test points LM1-LM9. It is shown that, for the point LM1, it is possible to detect lepton-flavor violation in neutralino decays with lepton-flavor-violating branching Br( → μ^± e ^∓ ) ≥ 0.04 Br( → e ⁺ e ⁻ , μ⁺ μ⁻ ) for an integral luminosity of 10 fb⁻¹. The discovery potential in the mSUGRA-SUSY scenario with tan β = 10, sgn(μ) = + in the (m ₀, m _1/2) plane using the e ^± μ^∓ + E _T ^miss signature is determined. The text was submitted by the authors in English.     

Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

CP-violating effects inZ decays to τ leptons

We calculate CP-odd correlations inZ decays to leptons, . These correlations are sensitive to the weak dipole moment of the . With 10⁷ producedZ particles and with observation of the decay channels and v we estimate that can be determined with an accuracy of about (1 s.d.).     

Fourier transform of supermeasures

In the note, a Smolyanov-Shavgulidze model of infinite-dimensional superspace H _Λ = Λ₀ H ₀ ⊕ Λ₁ H ₁ corresponding to a Hilbert space H = H ₀ ⊕ H ₁ over a Hilbert superalgebra Λ = Λ₀ ⊕ Λ₁ is considered. Its relation to the Khrennikov superspace is discussed. Moreover, H _Λ is equipped with the structure of Hilbert superspace with an inner superproduct (·, ·)_Λ. The supermeasures are defined as Λ^ℂ (∧H ₁)-valued measures on H ₀ (Λ^ℂ stands for the complexification of Λ). The definition of the Fourier supertransform is similar to the ordinary one, (y) = μ(dz). It turns out that the values of the Fourier supertransform of a supermeasure on the subspace = H ₀ ⊕ Λ₁ H ₁ can be obtained by applying a certain operator to the values of the classical Fourier transform. The main result is the theorem claiming that the Fourier supertransform of supermeasures is isometric on superspaces with zero even part (H ₀ = {0}). As a corollary, we note that the operator of Fourier supertransform is injective. We also give necessary and sufficient conditions for the countable additivity of cylindrical supermeasures in terms of continuity of their Fourier supertransforms (an analog of the Minlos-Sazonov theorem).     

Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions

We have investigated bound state solutions of the Schrodinger equation for one-dimensional harmonic oscillator potential together with even number of Dirac delta functions. These point interactions are located at symmetric points x = x _i and x = −x _i (i = 1, 2,..., N) and they have complex conjugate strengths and , respectively. We present explicit forms of eigenfunctions and an algebraic eigenvalue equation and numerical solutions for this -symmetric Hamiltonian. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Orthogonality theorem for a one-dimensional-electron gas with a bounded spectrum

The overlap between the ground-state wave functions of a one-dimensional electron gas with the Hamiltonians Ĥ ₀ and , where is the impurity potential, is calculated. It is shown that in the limit of an infinite potential the overlap vanishes as M ^−1/8 as M→∞, where M is the number of filled levels, while in the case of a weak potential this overlap differs little from 1. A relation is found between the magnitude of the overlap and the behavior of the density of states near the Fermi energy (statistics of the levels). The possibility of linearization of the spectrum and the possibility of performing a bosonization procedure are discussed in light of the results obtained. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 57–60 (10 July 1996)     

Bounds on neutrino mixing with exotic singlet neutrinos

We examine the effects of mixing induced non-diagonal light-heavy neutrino weak neutral currents on the amplitude for the process (with a=e, μ or τ). By imposing constraint that the amplitude should not exceed the perturbative unitarity limit at high energy , we obtain bounds on light-heavy neutrino mixing parameter sin² where is the mixing angle. In the case of one heavy neutrino (mass mξ) or mass degenerate heavy neutrinos, for Λ=1 TeV, no bound is obtained for mξ<0.50 TeV. However, sin² ≤3.8 × 10⁻⁶ for mξ=5 TeV and sin ≤6.0 × 10⁻⁸ for mξ=10 TeV. For Λ=∞, no constraint is obtained for mξ<0.99 TeV and sin² ≤3.8 × 10⁻² (for mξ=5 TeV) and sin² ≤9.6 × 10⁻³ (for mξ=10 TeV).     

Superconductor-insulator duality for an array of Josephson wires

A novel model system is proposed for the study of superconductor-insulator transitions that is a regular lattice whose each link consists of a Josephson-junction chain of N ≫ 1 junctions in sequence. The theory of such an array is developed for the case of semiclassical junctions with the Josephson energy E _J larger compared to the Coulomb energy E _C = e ²/2C of the junctions. An exact duality transformation is derived that transforms the Hamiltonian of the proposed model into a standard Hamiltonian of a JJ array. The nature of the ground state is controlled (in the absence of random offset charges) by the parameter q ≈ N ² exp with the superconductive state corresponding to small q < q _c . The values of q _c are calculated for magnetic frustrations f = 0 and f = 1/2. The temperature of the superconductive transition T _c (q) and q < q _c is estimated for the same values of f. In the presence of strong random offset charges, the T = 0 phase diagram is controlled by the parameter ; the critical value and the critical temperature at zero magnetic frustration are estimated. The text was submitted by the authors in English.     

n - \bar n transitions in nuclei and mixing of nuclear states with A and A−22

A new lower limit on the period of oscillations, sec, which follows from the stability of Fe, is found. This limit is almost 10 times larger than previous estimations. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 7, 456–461 (10 October 1996) This paper is an extended version of the talk presented at the Workshop on Baryon Instability Searches, Oak Ridge, March 1996. Published in English in the original Russian journal. Edited by Steve Torstveit.     

A study of the nuclear-medium influence on neutral-strange-particle production in deep-inelastic neutrino scattering

The influence of nuclear effects on the production of neutral strange particles (V ⁰) is investigated using the data obtained with SKAT propane-freon bubble chamber irradiated in the neutrino beam (with E _v =3−30 GeV) at the Serpukhov accelerator. The mean multiplicity of V ⁰ particles in nuclear interactions, , is found to exceed significantly that in “quasideuteron” interactions, . The ratio of is larger than that for π⁻ mesons, . It is shown that the multiplicity gain of V ⁰ particles can be explained by intranuclear interactions of produced pions. The text was submitted by the authors in English.